Application of a nudging technique to thermoacoustic tomography

Xavier Bonnefond (1) , Sébastien Marinesque (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

ThermoAcoustic Tomography (TAT) is a promising, non invasive, medical imaging technique whose inverse problem can be formulated as an initial condition reconstruction. In this paper, we introduce a new algorithm originally designed to correct the state of an evolution model, the \emph{back and forth nudging} (BFN), for the TAT inverse problem. We show that the flexibility of this algorithm enables to consider a quite general framework for TAT. The backward nudging algorithm is studied and a proof of the geometrical convergence rate of the BFN is given. A method based on Conjugate Gradient (CG) is also introduced. Finally, numerical experiments validate the theoretical results with a better BFN convergence rate for more realistic setups and a comparison is established between BFN, CG and a usual inversion method.

Mots clés: thermoacoustics; tomography; medical; imaging; wave equation; reversible; nudging; control; back and forth

Domaines: Optimisation et contrôle [math.OC]

Xavier Bonnefond, Sébastien Marinesque. Application of a nudging technique to thermoacoustic tomography. 2010. ⟨hal-00647917⟩